INDUCTION ON ANY GIVEN CONDUCTOR. 573 



curve. The action on the point A in the case of an unlimited plane, 

 will still have a vertical component, another directly opposed to the 

 motion, and a third perpendicular to the trajectory of the pole, and 

 directed towards the concavity of the curve. 



589. DAMPING OF COMPASS NEEDLES. The action of a con- 

 ducting disc on a magnetic system in motion is used in compasses, 

 and galvanometers, to deaden the oscillations of needles, in the form 

 in which the phenomenon was first observed by Gambey. 



This reciprocal action is equivalent to a kind of friction which 

 hinders the relative movement of the two systems ; from this follows 

 an absorption of energy which exactly corresponds to the heating of 

 the conductor by induced currents. 



590. INDUCTION ON ANY GIVEN CONDUCTOR. More generally, 

 whenever a conductor of any given form is displaced in a magnetic 

 field, induced currents result, which oppose the motion j but the 

 calculation of the effects of induction presents in that case the 

 greatest difficulties, for the three dimensions of the conductor come 

 into play. Faraday observed in this way that if a copper cube 

 suspended by a thread is placed between the poles of an electro- 

 magnet and is made to rotate rapidly, the cube will stop when 

 a current passes through the coils, and a considerable resistance 

 is experienced to its being made to rotate again. 



Foucault conceived the idea of utilising this experiment to 

 render evident the heating of a conductor. By means of a system 

 of toothed wheels worked by a handle, he maintains a conducting 

 disc in rotation between the poles of a very powerful electromagnet ; 

 the work expended is considerable, and the temperature of the disc 

 rises very rapidly. The measurement of the work expended, and 

 of the corresponding heat even furnishes a means of determining 

 the mechanical equivalent of heat; this is the principle of the 

 method used by M. Violle. 



